The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field

Taubes, Clifford Henry

doi:10.2140/gt.2009.13.1337

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The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field

Clifford Henry Taubes

Geometry & Topology 13 (2009) 1337–1417

DOI: 10.2140/gt.2009.13.1337

Abstract

Let $M$ denote a compact, orientable 3–dimensional manifold and let a denote a contact 1–form on $M$ ; thus a $\land$ da is nowhere zero. This article explains how the Seiberg–Witten Floer homology groups as defined for any given ${Spin}_{ℂ}$ structure on $M$ give closed, integral curves of the vector field that generates the kernel of $d a$ .

Mathematical Subject Classification 2000

Primary: 57R17, 57R57

References

Publication

Received: 22 April 2007

Revised: 24 November 2008

Accepted: 1 December 2008

Published: 16 February 2009

Proposed: Tom Mrowka

Seconded: Yasha Eliashberg, Ron Stern

Authors

Clifford Henry Taubes
Department of Mathematics Harvard University Cambridge MA 02138 USA

Volume 13, issue 3 (2009)